OOIR: Observatory of International Research

Papers

(The TQCC of American Mathematical Monthly is 0. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2022-05-01 to 2026-05-01.)

Article	Citations
Reviews	7
The Mathematical Community Working To Create Better (And Free!) Textbooks	7
Problems and Solutions	7
100 Years Ago This Month in The American Mathematical Monthly	6
The Altitudes of a Triangle	5
100 Years Ago This Month in The American Mathematical Monthly	5
My Friend Abe Shenitzer	5
Polynomial Approximations to Continuous Functions	5
A Generalization of Schatunowsky’s Theorem	4
Six Houses and Three Utilities on A Coffee Mug	4
Problems and Solutions	4
A Dynamic Kelly Criterion for Games with a Maximum Payout	4
Lucky Cars: Expected Values and Generating Functions	3
100 Years Ago This Month in The American Mathematical Monthly	3
Reviews	3
How to Prove it with Lean	3
On Erdős’s Proof of the Existence of Cages	3
Romance of Mathematics	3
An Elementary Solution of the Basel Problem	3
In Search of Comrade Agronomof: Some Tribonacci History	3
Pentagram Configurations for Pentagons and Hexagons	3
Problems and Solutions	3
Tiling with Monotone Polyominos	3
A Number System with Base	3
Optimizing for the Rupert Property	3

Reviews	2
Honsberger-Type Identities via Busche-Ramanujan Identity	2
Alice and Bob on ????: Reversal, Coupling, Renewal	2
A New Polygonal Number Theorem	2
On the Chromatic Number of the Plane with Two Forbidden Distances	2
Moments in the Exact Summation of the Curious Series of Kempner Type	2
Galileo’s Swiftest Descent Problem Revisited: Complete Analytic Solution	2
Faculty Seminar	2
Averages in Projectile Motion with Linear and Quadratic Drag	2
The Paul R. Halmos–Lester R. Ford Awards for 2024	2
On Liouville’s Theorem for Conformal Maps	2
Reviews	2
A Non-Terminating Game of Beggar-My-Neighbor	2
Three Proofs of the Spectral Theorem That You Might Not Know About	2
A Tale of Two Cyclicities: Counting in Finite Cyclic Groups and Finite Fields	2
Problems and Solutions	2
Problems and Solutions	2
Does the Convex Order Between the Distributions of Linear Functionals Imply the Convex Order Between the Probability Distributions Over ℝ ^d	2
A New Theorem for Mixed Partial Derivatives	2
On a Geometry Problem in Plato’s Meno	2
A Combinatorial Proof of the Existence of Dense Subsets in ℝ without the “Steinhaus” like Property	2
The Discrete Theorema Egregium	2
The Binomial Coefficient as an (In)finite Sum of Sinc Functions	1
A Shortcut to the Cauchy Integral Theorem	1
The Simplest Unlimited-Player Game of Skill	1
Problems and Solutions	1
The Genius of Gaudí: Geometry and Architecture	1
Problems and Solutions	1
The Infinitude of the Primes and Some Coloring Theorems	1
Five or Ten New Proofs of the Pythagorean Theorem	1
Problems and Solutions	1
Continuous Maps Admitting No Tangent Lines: A Centennial of Besicovitch Functions	1
A Third Real Solution to x=x⁻¹, Not Really	1
Summation Using an Expected Value Identity	1
Emergence of the Golden Angle in Flower Heads	1
On the Cayley-Hamilton Theorem	1
100 Years Ago This Month in The American Mathematical Monthly	1
Fourier Series for Nonperiodic Functions	1
Problems and Solutions	1
Retracing the Turns of the Archimedean Spiral	1
A Derivation of the Infinitude of Primes	1
Problems and Solutions	1
Diagonalization Games	1
A Thābit-like Extension of the Pythagorean Theorem	1
100 Years Ago This Month in The American Mathematical Monthly	1
Problems and Solutions	1
Editor’s Endnotes	1
Euclidean Rings of S -integers in Complex Quadratic Fields	1
Water-Based Proof of Jensen’s Inequality	1
Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts	1

The Poetry of Category Theory	1
On the Primorial Counting Function	1
Sports Analytics Double Take: The Need for Multiple Perspectives on Data	1
Parallel Sections of a Convex Body by Planes Tangent to an Inner Sphere	1
A Generalization of the Fan-Glicksberg Fixed Point Theorem	1
A Lebesgue Integral Variant of the Additive Square Problem	1
Which Finite Rings Have the Most or Fewest Units?	1
An Inequality of a Matrix with a Unit Vector	1
Parallelogram Law and Sum of Squares	1
A Model for Birdwatching and other Chronological Sampling Activities	1
Stirling’s Formula Without Calculus	1
100 Years Ago This Month in The American Mathematical Monthly	1
A Geometric Summation of the Geometric Series	1
Embeddings of K ₅ in the Torus	1
Topology Meets Number Theory	1
100 Years Ago This Month in The American Mathematical Monthly	1
Monthly Referees for 2022	1
Sharp Effective Finite-Field Nullstellensatz	1
George Bruce Halsted’s Non-Euclidean Pilgrimage to Hungary in 1896	1
Mathematics professors’ evaluation of students’ proofs: A complex teaching practice	1
More on the Cauchy–Schwarz Inequality	1
100 Years Ago This Month in The American Mathematical Monthly	1
Problems and Solutions	1
100 Years Ago This Month in The American Mathematical Monthly	1
100 Years Ago This Month in The American Mathematical Monthly	1
On the Divisibility of a Polynomial by One of its Derivatives	1
Launching a Data Analytics Major: How Collaboration and Agility Built a Successful Program	1
Discrete Calculus and Weighted Fibonacci and Tribonacci Sums	1
The Eighty-Second William Lowell Putnam Mathematical Competition	1
Yet Another Proof of the Strong Law of Large Numbers	1
Problems and Solutions	1
Following in Yiu’s Footsteps but on the Eisenstein Lattice	1
Integers as Sums of Four Tetrahedral Numbers and Eight Pentatope Numbers in One Identity	1
L-Tetromino Tilings and Two-Color Integer Compositions	0
Problems and Solutions	0
You Probably Won’t Believe It, But 3(1+φ − φ⁻¹) = 3!	0
The Fundamental Theorem of Algebra via Real Polynomials	0
Diversity, Identity, and Data	0
Problems and Solutions	0
A Special Form of Slower Divergent Series	0
Unlocking Your Bike the Easy Way	0
Regular Matchstick Graphs on the Sphere	0
Community and Belonging in Mathematics*	0
Spandrelized Tilings	0
Divisibility Graphs and Modular Multiplication Tables	0
Odd-Period Cycles of the Logistic Map	0
Freely Independent Coin Tosses, Standard Young Tableaux, and the Kesten–McKay Law	0
An Elementary Proof of the Layer Cake Representation Theorem	0
Browder’s Theorem through Brouwer’s Fixed Point Theorem	0
What Is the Shape of a Cupola?	0
Problems and Solutions	0
Problems and Solutions	0
A Conjecture on Primes in Arithmetic Progressions and Geometric Intervals	0
A Friendly Guide to the Real Exponential Function	0
Ten Points on a Cubic	0
A Simple Closed-Form Approximation to the Prime-Counting Function	0
Duelling Idiots and Abel Sums	0
New Primality Criterion Based on Lucas Sequences	0
Reviews I Died for Beauty: Dorothy Wrinch and the Cultures of Science . By Marjorie Senechal, Oxford University Press, 2012. 312 pp., ISBN 978-0199732593, $57.00.	0
100 Years Ago This Month in The American Mathematical Monthly	0
Reviews	0
What Do Networks and Elliptic Curves Have in Common?	0
A More Malicious Maitre d’	0
Introduction to Quantum Algorithms	0
Advanced mathematical knowledge in teaching practice: Perceptions of secondary mathematics teachers	0
Geometric Graphs with Exponential Chromatic Number and Arbitrary Girth	0
Modeling & Optimization for Streaming Listening Demand	0
Enhanced Bounds for Divided Differences and the Error in Polynomial Interpolation	0
An Increasing Function with a Discontinuous Derivative	0
A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode	0
On 2025 and Other Torn Numbers	0
N-Player Final-Offer Arbitration: Harmonic Numbers in Equilibrium	0
A Simple Construction of Fat Cantor Sets	0
Around the GCD of the Values of Two Polynomials	0
100 Years Ago This Month in The American Mathematical Monthly	0
Reviews	0
Lucky Cars and the `Quicksort` Algorithm	0
Inscribing Spheres in Topologically Embedded Simplices	0
A Friendly Introduction to Path Algebras and Quiver Representations	0
Pythagorean Boxes and Quotients of Gaussian Integers	0

What Can You Draw?	0
An Equilateral Triangle of Side > n Cannot be Covered by n ² + 1 Unit Equilateral Triangles Homothetic to it	0
Reviews Graph Theory in America: The First Hundred Years . By Robin Wilson, John J. Watkins, and David J. Parks, Princeton University Press, 2023. 320 pp., ISBN 978-0691	0
Reviews	0
The Subseries are Dense in the Basel Problem	0
Wolstenholme’s Congruence for Lucas Sequences	0
Excavating and Analyzing Mathematics in the Mary Somerville Collection, Oxford	0
A Remarkable Summation Formula, Lattice Tilings, and Fluctuations	0
The Possible Asylum	0
“The Riddle of the Ages”: James Joseph Sylvester and the Transcendence of π	0
Asymptotics of Redistricting the n × n Grid	0
Counting Zeros of Random Functions	0
Collective Evolution Under Catastrophes	0
On the Complex Descartes Circle Theorem	0
How Many Homeomorphisms are “Many Homeomorphisms”?	0
On Nonnegativity of the Generalized Discriminants of Quadratics	0
The Intermediate Value Theorem for Linear Transformations	0
Revisiting the Lind–Reichardt Counterexample to Hasse’s Local-Global Principle	0
Equi-Triangulation of Polygons	0
Integration of Gauß-Type Functions in Finite Terms	0
An Upper Bound on the Size of Sidon Sets	0
Some Applications of the Maynard–Tao Theorem	0
When Will (Game) Wars End?	0
Correction	0
Using a SAT Solver to Find Interesting Sets of Nonstandard Dice	0
Gagliardo-Nirenberg-Sobolev Inequality: An Induction Proof	0
Euclid after Computer Proof-Checking	0
Solving Algebraic Equations by Completing Powers	0
Newton’s Method Without Division	0
An Upper Bound on the Divisor Counting Function	0
Reviews	0
Reviews	0
A Piecewise-Linear Fixed Point Theorem	0
The Area Under the Witch of Agnesi	0
The Factor Ring Structure of Quadratic Principal Ideal Domains	0
Testing Whether a Table Defines a Group	0
A Pigeon Hole Proof of the Infinitude of Primes	0
Triangle Inequalities Indexed by Graphs	0
The Paul R. Halmos–Lester R. Ford Awards for 2022	0
Conway’s Spiral and a Discrete Gömböc with 21 Point Masses	0
A Second Raabe’s Test and Other Series Tests	0
Reviews	0
On the Topology of Punctured Spaces	0
Reviews	0
Problems and Solutions	0
Reviews	0
Archive Labeling Sequences	0
Euler’s Inequality for Circumradius and Inradius	0
100 Years Ago This Month in The American Mathematical Monthly	0
Finite Abelian Groups via Congruences	0
Problems and Solutions	0
Invariance of the Area and Volume of Cycloid Surfaces and Trochoid Surfaces	0
On Parking Functions and The Tower of Hanoi	0
Problems and Solutions	0
Calculating Prodigies in the Nineteenth Century: Science as Spectacle or Real Skill?	0
Sums of Two Squares Visualized	0
Ghostly Irrational Numbers	0
Celebrating Herbert Slaught’s “Romance of Mathematics”	0
An Exact Bound for the Inner Product of Vectors in ℂ ⁿ	0
Frobenius Integrability, Automotive Blind Spots, Non-reversing Mirrors, and Panoramic Mirrors	0
100 Years Ago This Month in The American Mathematical Monthly	0
A Quixotic Proof of Fermat’s Two Squares Theorem for Prime Numbers	0
Travel in an Infinite Desert	0
A Remark on the Ratio of Consecutive Primes	0
The Birational Geometry of Ceva’s Theorem	0
A New Perspective on Impartial and Unbiased Apportionment	0
The Simplest Polynomial Differential Systems in ℝ ³ Having an Invariant Sphere	0
Is AX = Y Possible with a Positive Definite A ?	0
Vieta’s Formula, the Fabius Function and the Partition Function	0
An Arithmetic-Geometric Proof of the Arithmetic-Geometric Inequality	0
Invariance of the Cauchy Family Under Linear Fractional Transformations	0
Classification of d for Which the Period Length of the Continued Fraction Expansion of √d is Odd	0
Problems and Solutions	0
Laws of Exponents by Differentiation	0
Intrinsic Geometries of the Simple Group of Order 168	0
Convex Bodies with Equipotential Circles	0
Math Games With Bad Drawings: 75 Simple, Challenging, Go-Anywhere Games—And Why They Matter	0
Legendre’s Singular Modulus	0
From Abel’s Binomial Theorem to Cayley’s Tree Formula	0
Complex Numbers as Powers of Transcendental Numbers	0
Encyclopedia of Knot Theory	0
The Green-Tao Theorem and the Infinitude of Primes in Domains	0
On Subprime Recurrences	0
A Canonical Group-Like Structure on the Spanning Trees of a Plane Graph	0
Problems and Solutions	0
Problems and Solutions	0
Lagrange Inversion Formula by Induction	0
Regular Patterns of Quadratic Residues	0
A Napoleon-like Theorem for Quadrilaterals	0
AGM and Jellyfish Swarms of Elliptic Curves	0
Approximating Complex Numbers by Roots of Integral Irreducible Polynomials	0
If R ^m ≅ R	0
How to Tee a Hyperplane	0
A Short Proof for the Volume of Square Pyramids	0
Reviews	0